The official airport website states that the airport is 18km (about 11 miles) from Las Palmas.
The fare to Parque San Telmo, in Las Palmas, is given as €23.55 from 0600 to 2200, and €26.71 from 2200 to 0600 (or on public holidays). The fare to Parque Santa Catalina, a bit further into Las Palmas, is given as €31.04 (day) or €35.21 (night/holidays).
Source:
http://www.aena.es/cs...0196&pagename=subHome
Bus service 60 will also get you to Las Palmas. It runs every 15 minutes for most of the day:
http://www.globalsu.net/es/pdf/linea60.pdf
The fare is €2.10
Chris